Finite temperature properties of the Dirac operator under local boundary conditions

TL;DR

This paper investigates the finite temperature behavior of Dirac operators in a one-dimensional segment with local boundary conditions, focusing on spectral asymmetry and its impact on the fermion free energy and number.

Contribution

It provides a detailed analysis of how local boundary conditions influence the spectral properties and finite temperature characteristics of Dirac fields in one dimension.

Findings

Spectral asymmetry affects the zeta-regularized determinant.

Boundary conditions alter the finite temperature free energy.

Spectral contributions are explicitly computed for specific boundary conditions.

Abstract

We study the finite temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under two different members of the family of local boundary conditions defining a self-adjoint Euclidean Dirac operator in two dimensions. For one of such boundary conditions, compatible with the presence of a spectral asymmetry, we discuss in detail the contribution of this part of the spectrum to the zeta-regularized determinant of the Dirac operator and, thus, to the finite temperature properties of the theory.